Problem: Rewrite as a simplified fraction. ${1.1\overline{89} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1189.8989...\\ 10x &= 11.8989...\end{align*}}$ Subtracting the two equations, we have: ${990x = 1178}$ ${x = \dfrac{1178}{990}} $ ${x = \dfrac{589}{495}} \text{or} {1 \dfrac{94}{495}}$